The length of a box is 36 cm. If you cut the length equally into 3 parts, the surface area will increase 120 cm^2. What is the volume of the box?

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Answer 1 · 2018-05-23T00:23:57

$1080 c m^{3}$ $1080cm^3$

so we cut the box in 3 parts each on is:

$\frac{36 c m}{3} = 12 c m$ $(36 cm)/3 = 12 cm$ long:

When we cut the box twice that adds 4 new surface areas, 2 at each cut that equal a total of 120 so each end will be:

$\frac{120 c m^{2}}{4} = 30 c m^{2}$ $(120 cm^2)/4 = 30cm^2$

So now we have 3 boxes that are $12 c m$ $12 cm$ long with bases $30 c m^{2}$ $30 cm^2$

$V_{box} = l \cdot w \cdot h$ $V_"box" = l*w*h$

$A_{base} = l \cdot w$ $A_"base" = l*w$

putting these together:

$V_{box} = A_{base} \cdot h$ $V_"box" =A_"base"*h$

$V_{box} = 30 c m^{2} \cdot 12 c m = 360 c m^{3}$ $V_"box" =30cm^2*12cm = 360cm^3$

Finally since there are 3 boxes:

$3 \cdot 360 c m^{3} = 1080 c m^{3}$ $3*360cm^3=1080cm^3$